Background: I took multiple statistics classes in both high school and college, but nothing I learned ever stuck. The problem is, things like p-tests, the equations for chi-squared/normal distributions, even the standard deviation are always simply presented as fact, without any proof/justification/motivation for why this equation/method is the correct one.

Often, this is because the books are written for people looking to simply apply statistics rather than truly understand it. Usually, not even a calculus-background is assumed, despite the underlying equations being calculus-heavy.